Higher Order Orthogonal Tensor SVD And Its Application To Incremental Recommendation

With the development of information technology,the data generated on the network growth explosive,this directly led to the problem of information overload.Although the network information is more and more extensive and comprehensive,but because of the amount of data,users cost more and more to find the target information.The recommendation system helps users quickly find target information and reduce the cost of finding information for users.As a tool to express high-dimensional space,tensor has the advantage of expressing high-dimensional heterogeneous data.Tensor has been widely used in data mining,graph computing and other fields.With the development of Internet derivatives,a variety of social networks and intelligent devices produce a large number of heterogeneous data.The use of tensor to express the data and with the use of HOSVD decomposition to do the recommendation has become the focus of current study now.HOSVD(High Order Singular Value Decomposition)decompose the original tensor in accordance with the various models,which not taking into account the impact of multiple modules.Different dimensions of the actual data may be related.Based on the decomposition of HOSVD,this paper introduces a novel tensor decomposition method,HO-OTSVD(Higher Order Orthogonal Tensor SVD),which decomposes an Nth order tensor into a core tensor an N adjunct orthogonal tensor.Using the relationship between OTSVD(Orthogonal Tensor SVD)and matrix SVD,We proposed a higher order orthogonal decomposition algorithm suitable for large sparse tensor based on the bi-diagonalized lanczos method.Aiming at the characteristics of streaming applications,we studied the relationship between incremental unfolding and original tensor unfolding and proposed the incremental calculation method of HO-OTSVD.The incremental algorithm reduces the unnecessary repetitive calculation,while reducing the system memory capacity requirements,improve the efficiency of decomposition.The recommendation model based on HO-OTSVD is proposed,and the finely grained user-context-object is recommended by the decomposition model of HO-OTSVD.The model is validated on the purchase record data set of the Taobao users,and the efficiency of the incremental algorithm is analyzed.